CALIFORNIA STATE POLYTECHNIC UNIVERSITY AT POMONA DEPARTMENT OF MECHANICAL ENGINEERING Theory & Design for Mechanical Measurements Laboratory ME 435L Lab Manual Revised and Updated Winter 2006 by Dr. Kevin R. Anderson Associate Professor Mechanical Engineering ME 435L DirectorCALIFORNIA STATE POLYTECHNIC UNIVERSITY AT POMONA DEPARTMENT OF MECHANICAL ENGINEERING 2 Table of Contents Pressure Transient Fourier Analysis Experiment………...……….……..03 NI-ELVIS Operational Amplifier Experiment...……...…………………12 Thermal Conductivity Measurement Experiment…….………………....20 Fin Heat Loss Experiment……………………………………………….26 REVISION Winter 2006 (Note: this laboratory manual is a work in progress, this version supersedes all previous versions and the material in this manual is subject to change at any time based upon the motivation of author)CALIFORNIA STATE POLYTECHNIC UNIVERSITY AT POMONA DEPARTMENT OF MECHANICAL ENGINEERING 3 PRESSURE TRANSIENT FOURIER ANALYSIS EXPERIMENT Objectives 1. To calibrate a typical strain gage pressure transducer. 2. To determine by Fourier Analysis (harmonic analysis) the equation for a fluid dynamic transient curve and to compare the experimentally determined curve with a computer generated curve so as to determine the number of harmonics necessary to obtain reasonable accuracy. Discussion The transient flow of incompressible fluids in ducts of constant area is of importance in many fields of engineering. The fundamental significance of solving problems involving transient flow phenomena is that such solutions provide a complete history of the flow field and allow for detailed interpretation of how steady state conditions were obtained, and why certain characteristics and phenomena dominate once steady state conditions do exist. The fluid dynamic principles involved in conducting such transient studies are not within the framework of this course. We are, however, concerned with instrumentation and the proper evaluation of data obtained by means of mechanical measurements resulting from such studies. Of such concern here are the resulting dynamic (transient in this case)CALIFORNIA STATE POLYTECHNIC UNIVERSITY AT POMONA DEPARTMENT OF MECHANICAL ENGINEERING 4 output signals. Such signal information as the fundamental frequency, the harmonic components with their relative amplitudes, frequencies, and phase relations are often requested from the recorded waveform. This type of information is most easily obtained by performing a harmonic analysis of the output signal. The principle of a Fourier Analysis is that a given arbitrary function of a real variable, time in this case, can be represented as a sum of sine and cosine functions in which amplitudes of the functions are determined by the Fourier Analysis (see sections 2.4 and 2.5 of Reference 1). The time period in this experiment corresponds to the time period from initiation of flow to the completion of one full cycle of the pressure transient. A mathematical representation of the amplitudes to be determined in the present problem would appear as shown in the equation below, where )( trpδp(t) is the pressure obtained by the experiment, and the remaining symbols defined in Reference 1: ==−=NrkN,kNkrjtrpNfp12/,,21 );/ 2 exp() (2)( πδ A computer program then solves for the coefficients of the sine and cosine functions. The program performs the DFT calculation described in Reference 1, Section 2.5. Equipment 1. Pressure transducer – Strain Gage type 2. Op Amplifier Circuit Board 3. Flow initiation supply tank 4. HP 34970A Data Acquisition/ Switch Unit 5. HP 35670A Dynamic Signal Analyzer References 1. Figliola and Beasley, “Theory and Design for Mechanical Measurements”, 4th Ed., Wiley, 2006 Useful Conversion Constant (1 in. H2O = 0.036136 psi = 249.082 N/m2) Procedure 1. Acquire Calibration Curve Data a) Fill the sight glass of the tank to 10 inches b) Measure the voltage across the un-amplified input of the Op-Amp board. Hold the arrow key on the HP 34970A to freeze the voltage reading, so that you can write it down on your lab sheet.CALIFORNIA STATE POLYTECHNIC UNIVERSITY AT POMONA DEPARTMENT OF MECHANICAL ENGINEERING 5 c) Release 1 inch of water form the sight glass and repeat voltage measurement of part b) until sufficient data has been gathered (4 or 5 points should suffice) d) Make note of the manufacturer’s calibration data shown in the data sheet attached to the pressure transducer Viatran Model 119 Pressure Transducer 2. Acquire Pressure Transient Data a) Fill the flow initiation supply tank to ten inches depth. Use the sight glass and ruler attached to the tank. b) Connect BNC connection from Operational Amplifier Circuit to Channel 1 of HP 35670A Dynamic Signal Analyzer c) Turn on Signal Analyzer by pushing the small white button at lower left hand corner of display d) Turn off the HP 34970A Data Acquisition Unit before proceeding to the next step Agilent HP 35670A Dynamic Signal Analyzer Initialize the Analyzer a) Press the green [Preset] hardkey on the AnalyzerCALIFORNIA STATE POLYTECHNIC UNIVERSITY AT POMONA DEPARTMENT OF MECHANICAL ENGINEERING 6 b) Press [DO PRESET] softkey (F1) c) Press the [System Utility] hardkey d) Press the [Auto Calibration] softkey (F2) to toggle Auto-Cal OFF e) Press [Inst Mode] hardkey f) Press [CHANNELS 1 2 4] softkey (F7) until 1 is highlighted Set the Record Time Length a) Select the time record length b) Press the [Freq] hardkey c) Press the [RECORD LENGTH] softkey (F8) d) Enter 0.5 and then press the [S] softkey (F1) Display the Time Waveform a) Press the [Disp Format] hardkey b) Press the [SINGLE] softkey (F1) c) Press the [Active Trace] hardkey d) Press the [A] SOFTKEY (F1) e) Press the [Meas Data] hardkey f) Press the [CHANNEL 1 2 3 4] softkey (F1) until 1 is highlighted (make sure box around [CHANNEL 1 2 3 4] lights up) g) Press the [TIME CHANNEL 1] softkey (F5) Set Up Event Triggering a) Press the [Trigger] Hardkey b) Press the [CHANNEL 1 2 3 4] softkey (F3) until 1 is highlighted (make sure box around [CHANNEL 1 2 3 4] lights up) c) Press the [TRIGGER SETUP] softkey (F6) d) Press the [CHANNEL LEVEL]